- #1

RChristenk

- 63

- 9

- Homework Statement
- In how many ways can ##5## prizes be given away to ##4## boys when each boy is eligible for all the prizes?

- Relevant Equations
- Concepts in permutations

I first thought obviously the solution would be ##5^4##. This made intuitive sense to me because this solution means the first boy can choose one out of five prizes, the second boy can choose one out of five (even if it's the same prize as the first boy's since each boy is eligible for all prizes), and so on until the fourth boy. So in essence the exponent ##4## is the number of boys.

But the correct answer is the opposite: ##4^5##. This also makes sense. The first prize can be given to one of the four boys, the second prize can be given to one of the four boys (even if it's the first boy again since each boy is eligible for all prizes) and so on until the fifth prize. In this case the exponent would be the number of prizes.

Since both answers make intuitive sense, how can they be numerically different when both are dealing with four boys and five prizes? Where did I go wrong? Thanks.

But the correct answer is the opposite: ##4^5##. This also makes sense. The first prize can be given to one of the four boys, the second prize can be given to one of the four boys (even if it's the first boy again since each boy is eligible for all prizes) and so on until the fifth prize. In this case the exponent would be the number of prizes.

Since both answers make intuitive sense, how can they be numerically different when both are dealing with four boys and five prizes? Where did I go wrong? Thanks.